Apply a digital filter (direct form II transposed): Difference between revisions
Apply a digital filter (direct form II transposed) (view source)
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The signal that needs filtering is the following vector: [-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412, -0.662370894973, -1.00700480494, -0.404707073677 ,0.800482325044, 0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195, 0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293, 0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589]
;See also:
[[https://en.wikipedia.org/wiki/Butterworth_filter Wikipedia on Butterworth filters]]
=={{header|11l}}==
{{trans|Nim}}
<
V result = [0.0] * signal.len
L(i) 0 .< signal.len
Line 36 ⟶ 40:
L(r) result
print(‘#2.8’.format(r), end' ‘’)
print(I (L.index + 1) % 5 != 0 {‘, ’} E "\n", end' ‘’)</
{{out}}
Line 47 ⟶ 51:
=={{header|Ada}}==
<
procedure Apply_Filter is
Line 106 ⟶ 110:
Ada.Text_IO.New_Line;
end loop;
end Apply_Filter;</
=={{header|ALGOL 68}}==
{{Trans|C++}} ... via Yabasic<br>
... with the "j" loops transformed to not needlessly iterate beyond i.<br>
The default lower bound in Algol 68 arrays is 1, so the loops/subscripts have been adjusted accordingly.
<syntaxhighlight lang="algol68">
BEGIN # apply a digital filter #
# the lower bounds of a, b, signal and result must all be equal #
PROC filter = ( []REAL a, b, signal, REF[]REAL result )VOID:
IF LWB a /= LWB b OR LWB a /= LWB signal OR LWB a /= LWB result THEN
print( ( "Array lower bounds must be equal for filter", newline ) );
stop
ELSE
FOR i FROM LWB result TO UPB result DO result[ i ] := 0 OD;
FOR i FROM LWB signal TO UPB signal DO
REAL tmp := 0;
FOR j FROM LWB b TO IF i > UPB b THEN UPB b ELSE i FI DO
tmp +:= b[ j ] * signal[ LWB signal + ( i - j ) ]
OD;
FOR j FROM LWB a + 1 TO IF i > UPB a THEN UPB a ELSE i FI DO
tmp -:= a[ j ] * result[ LWB result + ( i - j ) ]
OD;
result[ i ] := tmp / a[ LWB a ]
OD
FI # filter # ;
[ 4 ]REAL a := []REAL( 1, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17 );
[ 4 ]REAL b := []REAL( 0.16666667, 0.5, 0.5, 0.16666667 );
[ 20 ]REAL signal
:= []REAL( -0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412
, -0.662370894973, -1.00700480494, -0.404707073677, 0.800482325044
, 0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195
, 0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293
, 0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589
);
[ 20 ]REAL result;
filter( a, b, signal, result );
FOR i FROM LWB result TO UPB result DO
print( ( " ", fixed( result[ i ], -9, 6 ) ) );
IF i MOD 5 /= 0 THEN print( ( ", " ) ) ELSE print( ( newline ) ) FI
OD
END
</syntaxhighlight>
{{out}}
<pre>
-0.152974, -0.435258, -0.136043, 0.697503, 0.656445
-0.435482, -1.089239, -0.537677, 0.517050, 1.052250
0.961854, 0.695690, 0.424356, 0.196262, -0.027835
-0.211722, -0.174746, 0.069258, 0.385446, 0.651771
</pre>
=={{header|AppleScript}}==
{{trans|Julia}} — except that j starts from 2 in the second inner repeat, there being no point in fetching and performing math with the zero about to be overwritten. This change in turn allows the result list to be populated on the fly instead of being pre-populated with zeros.
<syntaxhighlight lang="applescript">on min(a, b)
if (b < a) then return b
return a
end min
on DF2TFilter(a, b, sig)
set aCount to (count a)
set bCount to (count b)
set sigCount to (count sig)
set rst to {}
repeat with i from 1 to sigCount
set tmp to 0
set iPlus1 to i + 1
repeat with j from 1 to min(i, bCount)
set tmp to tmp + (item j of b) * (item (iPlus1 - j) of sig)
end repeat
repeat with j from 2 to min(i, aCount)
set tmp to tmp - (item j of a) * (item (iPlus1 - j) of rst)
end repeat
set end of rst to tmp / (beginning of a)
end repeat
return rst
end DF2TFilter
local acoef, bcoef, signal
set acoef to {1.0, -2.77555756E-16, 0.333333333, -1.85037171E-17}
set bcoef to {0.16666667, 0.5, 0.5, 0.16666667}
set signal to {-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412, ¬
-0.662370894973, -1.00700480494, -0.404707073677, 0.800482325044, ¬
0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195, ¬
0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293, ¬
0.025930339848, 0.490105989562, 0.549391221511, 0.9047198589}
DF2TFilter(acoef, bcoef, signal)</syntaxhighlight>
{{output}}
<syntaxhighlight lang="applescript">{-0.1529739895, -0.43525782905, -0.136043396988, 0.697503326548, 0.656444692469, -0.435482453256, -1.089239461153, -0.537676549563, 0.517049992313, 1.052249747155, 0.961854300374, 0.69569009401, 0.424356295096, 0.196262231822, -0.027835124463, -0.21172191545, -0.174745562223, 0.069258408901, 0.385445874308, 0.651770838819}</syntaxhighlight>
=={{header|C}}==
Given the number of values a coefficient or signal vector can have and the number of digits, this implementation reads data from a file and prints it to the console if no output file is specified or writes to the specified output file. Usage printed on incorrect invocation.
<syntaxhighlight lang="c">
#include<stdlib.h>
#include<string.h>
Line 224 ⟶ 318:
return 0;
}
</syntaxhighlight>
Input file, 3 lines containing first ( a ) and second ( b ) coefficient followed by the signal, all values should be separated by a single space:
<pre>
Line 243 ⟶ 337:
=={{header|C sharp|C#}}==
{{trans|Java}}
<
namespace ApplyDigitalFilter {
Line 284 ⟶ 378:
}
}
}</
{{out}}
<pre>-0.15297399, -0.43525783, -0.13604340, 0.69750333, 0.65644469
Line 295 ⟶ 389:
This uses the C++11 method of initializing vectors. In g++, use the -std=c++0x compiler switch.
<
#include <iostream>
using namespace std;
Line 346 ⟶ 440:
return 0;
}</
{{out}}
Line 353 ⟶ 447:
=={{header|Common Lisp}}==
{{trans|zkl}}
<
(defparameter b #(0.16666667L0 0.50000000L0 0.50000000L0 0.16666667L0))
(defparameter s #(-0.917843918645 0.141984778794 1.20536903482 0.190286794412 -0.662370894973
Line 368 ⟶ 462:
when (>= i j) sum (* (svref a j) (svref out (- i j)))))
(svref a 0)))
(format t "~%~16,8F" (svref out i)))</
{{out}}
<pre> -0.15297399
Line 394 ⟶ 488:
=={{header|D}}==
{{trans|Kotlin}}
<
alias T = real;
Line 440 ⟶ 534:
}
}
}</
{{out}}
Line 450 ⟶ 544:
=={{header|FreeBASIC}}==
{{trans|Yabasic}}
<
Dim As Integer j, k
Dim As Double tmp
Line 497 ⟶ 591:
Data 0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589
Sleep</
{{out}}
<pre>
Line 507 ⟶ 601:
=={{header|Go}}==
<
import "fmt"
Line 557 ⟶ 651:
fmt.Printf("%9.6f\n", v)
}
}</
{{out}}
<pre>
Line 584 ⟶ 678:
=={{header|Groovy}}==
{{trans|Java}}
<
private static double[] filter(double[] a, double[] b, double[] signal) {
double[] result = new double[signal.length]
Line 620 ⟶ 714:
}
}
}</
{{out}}
<pre>-0.15297399, -0.43525783, -0.13604340, 0.69750333, 0.65644469
Line 626 ⟶ 720:
0.96185430, 0.69569009, 0.42435630, 0.19626223, -0.02783512
-0.21172192, -0.17474556, 0.06925841, 0.38544587, 0.65177084</pre>
=={{header|Haskell}}==
The solution is based not on the explicit loops, as in strict imperative languages, but on lazy recursive trick known as "tying a knot".
<syntaxhighlight lang="haskell">import Data.List (tails)
-- lazy convolution of a list by given kernel
conv :: Num a => [a] -> [a] -> [a]
conv ker = map (dot (reverse ker)) . tails . pad
where
pad v = replicate (length ker - 1) 0 ++ v
dot v = sum . zipWith (*) v
-- The lazy digital filter
dFilter :: [Double] -> [Double] -> [Double] -> [Double]
dFilter (a0:a) b s = tail res
where
res = (/ a0) <$> 0 : zipWith (-) (conv b s) (conv a res)</syntaxhighlight>
=== Examples ===
Demonstration of convolution:
<pre>λ> take 10 $ conv [1,10,100,1000] [1..]
[1,12,123,1234,2345,3456,4567,5678,6789,7900]
</pre>
The given task:
<pre>λ> let a = [1, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17]
λ> let b = [0.16666667, 0.5, 0.5, 0.16666667]
λ> let s = [-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412, -0.662370894973, -1.00700480494, -0.404707073677, 0.800482325044, 0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195, 0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293, 0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589]
λ> dFilter a b s
[-0.15297398950031305,-0.4352578290502175,-0.13604339698849033,0.6975033265479628,
0.6564446924690288,-0.4354824532561055,-1.089239461152929,-0.5376765495627545,
0.517049992313214,1.0522497471553531,0.961854300373645,0.6956900940096052,
0.4243562950955321,0.19626223182178906,-2.7835124463393313e-2,-0.21172191545011776,
-0.17474556222276072,6.925840890119485e-2,0.3854458743074388,0.6517708388193053,
0.6802579154588558,0.326668188810626,-7.596599209379973e-2,-0.10888939616131928]
</pre>
The last line is redundant and appears due to the finiteness of a signal stream. The digital filter is able to handle infinite lists (as streams):
<pre>λ> take 10 $ dFilter a b $ cycle [1,-1]
[0.16666667,0.33333333000000004,0.11111111338888897,-0.11111110988888885,-3.703703775925934e-2,3.70370365925926e-2,1.2345679240740749e-2,-1.2345678851851824e-2,-4.1152264094650535e-3,4.115226279835409e-3]</pre>
=={{header|J}}==
There's probably a nicer way to do this:
<syntaxhighlight lang="j">Butter=: {{
t=. (#n) +/ .*&(|.n)\(}.n*0),y
A=.|.}.m
for_i.}.i.#y do.
t=. t i}~ (i{t) - (i{.t) +/ .* (-i){.A
end.
t%{.m
}}
sig=: ". rplc&('-_') {{)n
-0.917843918645, 0.141984778794, 1.20536903482,
0.190286794412,-0.662370894973,-1.00700480494,
-0.404707073677, 0.800482325044, 0.743500089861,
1.01090520172, 0.741527555207, 0.277841675195,
0.400833448236,-0.2085993586, -0.172842103641,
-0.134316096293, 0.0259303398477,0.490105989562,
0.549391221511, 0.9047198589
}}-.LF
a=: 1.00000000 _2.77555756e_16 3.33333333e_01 _1.85037171e_17
b=: 0.16666667 0.5 0.5 0.16666667
4 5$ a Butter b sig
_0.152974 _0.435258 _0.136043 0.697503 0.656445
_0.435482 _1.08924 _0.537677 0.51705 1.05225
0.961854 0.69569 0.424356 0.196262 _0.0278351
_0.211722 _0.174746 0.0692584 0.385446 0.651771</syntaxhighlight>
=={{header|Java}}==
{{trans|Kotlin}}
<
private static double[] filter(double[] a, double[] b, double[] signal) {
double[] result = new double[signal.length];
Line 666 ⟶ 833:
}
}
}</
{{out}}
<pre>-0.15297399, -0.43525783, -0.13604340, 0.69750333, 0.65644469
Line 675 ⟶ 842:
=={{header|Julia}}==
{{trans|zkl}}
<
rst = zeros(sig)
for i in eachindex(sig)
Line 692 ⟶ 859:
0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293,
0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589]
@show DF2TFilter(acoef, bcoef, signal)</
{{output}}<pre>DF2TFilter(acoef, bcoef, signal) = [-0.152974, -0.435258, -0.136043, 0.697503, 0.656445, -0.435482, -1.08924, -0.537677, 0.51705, 1.05225, 0.961854, 0.69569, 0.424356, 0.196262, -0.0278351, -0.211722, -0.174746, 0.0692584, 0.385446, 0.651771]</pre>
=={{header|Kotlin}}==
{{trans|C++}}
<
fun filter(a: DoubleArray, b: DoubleArray, signal: DoubleArray): DoubleArray {
Line 734 ⟶ 901:
print(if ((i + 1) % 5 != 0) ", " else "\n")
}
}</
{{out}}
Line 746 ⟶ 913:
=={{header|Lua}}==
{{trans|C++}}
<
local out = {}
for i=1,table.getn(input) do
Line 796 ⟶ 963:
end
main()</
{{out}}
<pre>-0.15297398950031, -0.43525782905022, -0.13604339698849, 0.69750332654796, 0.65644469246903, -0.43548245325611, -1.0892394611529, -0.53767654956275, 0.51704999231321, 1.0522497471554, 0.96185430037364, 0.6956900940096, 0.42435629509553, 0.19626223182179, -0.027835124463393, -0.21172191545012, -0.17474556222276, 0.069258408901195, 0.38544587430744, 0.65177083881931,</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<
a = {1.00000000, -2.77555756*^-16, 3.33333333*^-01, -1.85037171*^-17};
signal = {-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412, -0.662370894973, -1.00700480494, -0.404707073677, 0.800482325044, 0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195, 0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293, 0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589};
RecurrenceFilter[{a, b}, signal]</
{{out}}
<pre>{-0.152974,-0.435258,-0.136043,0.697503,0.656445,-0.435482,-1.08924,-0.537677,0.51705,1.05225,0.961854,0.69569,0.424356,0.196262,-0.0278351,-0.211722,-0.174746,0.0692584,0.385446,0.651771}</pre>
Line 810 ⟶ 977:
=={{header|MATLAB}}==
MATLAB is commonly used for filter design and implementation. To implement this filter, and display the original signal and the filtered result:
<syntaxhighlight lang="matlab">
signal = [-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412, -0.662370894973, -1.00700480494, -0.404707073677 ,0.800482325044, 0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195, 0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293, 0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589];
a = [1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17];
Line 827 ⟶ 994:
xlabel('n')
title('Filtered Signal')
</syntaxhighlight>
{{out}}
Line 844 ⟶ 1,011:
=={{header|Nim}}==
{{trans|Kotlin}}
<syntaxhighlight lang="nim">
import strformat
Line 874 ⟶ 1,041:
for i in 0..result.high:
stdout.write fmt"{result[i]: .8f}"
stdout.write if (i + 1) mod 5 != 0: ", " else: "\n"</
{{out}}
Line 884 ⟶ 1,051:
=={{header|Objeck}}==
{{trans|Java}}
<
function : Main(args : String[]) ~ Nil {
a := [1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17];
Line 924 ⟶ 1,091:
return result;
}
}</
{{output}}
Line 935 ⟶ 1,102:
=={{header|ooRexx}}==
<
a=.array~of(1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17)
b=.array~of(0.16666667, 0.5, 0.5, 0.16666667)
Line 971 ⟶ 1,138:
::OPTIONS digits 24 /* Numeric Digits 24, everywhere */
</syntaxhighlight>
{{out|output}}
<pre> 1 -0.152973989500
Line 996 ⟶ 1,163:
=={{header|Perl}}==
{{trans|Raku}}
<
use List::AllUtils 'natatime';
Line 1,027 ⟶ 1,194:
printf(' %10.6f' x 5 . "\n", @values);
}
</syntaxhighlight>
{{out}}
<pre> -0.152974 -0.435258 -0.136043 0.697503 0.656445
Line 1,038 ⟶ 1,205:
Note however that the a[j]* starts from index 2, unlike Julia/C/Raku/Rust/Sidef/zkl,
but the same as C++/C#/D/Java/Kotlin - and it does not seem to make any difference...
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">direct_form_II_transposed_filter</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">signal</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">result</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">signal</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">signal</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">tmp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">))</span> <span style="color: #008080;">do</span> <span style="color: #000000;">tmp</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">signal</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">))</span> <span style="color: #008080;">do</span> <span style="color: #000000;">tmp</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">result</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">result</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tmp</span><span style="color: #0000FF;">/</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">result</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">acoef</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1.00000000</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">2.77555756e-16</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3.33333333e-01</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1.85037171e-17</span><span style="color: #0000FF;">},</span>
<span style="color: #000000;">bcoef</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0.16666667</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.16666667</span><span style="color: #0000FF;">},</span>
<span style="color: #000000;">signal</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{-</span><span style="color: #000000;">0.917843918645</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0.141984778794</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1.20536903482</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0.190286794412</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">0.662370894973</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">-</span><span style="color: #000000;">1.00700480494</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">0.404707073677</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0.800482325044</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0.743500089861</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1.01090520172</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">0.741527555207</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0.277841675195</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0.400833448236</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">0.2085993586</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">0.172842103641</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">-</span><span style="color: #000000;">0.134316096293</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0.0259303398477</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0.490105989562</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0.549391221511</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0.9047198589</span><span style="color: #0000FF;">}</span>
<span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">direct_form_II_transposed_filter</span><span style="color: #0000FF;">(</span><span style="color: #000000;">acoef</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">bcoef</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">signal</span><span style="color: #0000FF;">),{</span><span style="color: #004600;">pp_FltFmt</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%9.6f"</span><span style="color: #0000FF;">,</span><span style="color: #004600;">pp_Maxlen</span><span style="color: #0000FF;">,</span><span style="color: #000000;">110</span><span style="color: #0000FF;">})</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
Line 1,065 ⟶ 1,235:
=={{header|Phixmonti}}==
{{trans|Phix}}
<
( 1.00000000 -2.77555756e-16 3.33333333e-01 -1.85037171e-17 ) var a
Line 1,088 ⟶ 1,258:
ps> a 1 get nip / ps> swap i set >ps
endfor
drop ps> ?</
{{out}}
<pre>[-0.152973989500313, -0.435257829050217, -0.13604339698849, 0.697503326547963, 0.656444692469029, -0.435482453256106, -1.089239461152929, -0.537676549562755, 0.517049992313214, 1.052249747155353, 0.961854300373645, 0.695690094009605, 0.424356295095532, 0.196262231821789, -0.0278351244633933, -0.211721915450118, -0.174745562222761, 0.0692584089011949, 0.385445874307439, 0.651770838819305]
Line 1,096 ⟶ 1,266:
=={{header|Python}}==
<
from __future__ import print_function
from scipy import signal
Line 1,118 ⟶ 1,288:
plt.plot(sig, 'b')
plt.plot(filt, 'r--')
plt.show()</
{{out}}
Line 1,129 ⟶ 1,299:
{{trans|C}} Strangely, C was more informative than Common Lisp in helping figure out what was going on here.
<
(define a (vector 1.00000000E0 -2.77555756E-16 3.33333333E-01 -1.85037171E-17))
Line 1,151 ⟶ 1,321:
filtered-signal)
(filter-signal-direct-form-ii-transposed a b s)</
{{out}}
Line 1,180 ⟶ 1,350:
{{trans|zkl}}
<syntaxhighlight lang="raku"
my @out = 0 xx @signal;
for ^@signal -> $i {
Line 1,202 ⟶ 1,372:
say TDF-II-filter(@signal, @a, @b)».fmt("% 0.8f")
Z~ flat (', ' xx 4, ",\n") xx *;</
{{out}}
<pre>(-0.15297399, -0.43525783, -0.13604340, 0.69750333, 0.65644469,
Line 1,213 ⟶ 1,383:
===version 1===
{{trans|Julia}}
<
@a= '1 -2.77555756e-16 3.33333333e-1 -1.85037171e-17' /*filter coefficients*/
@b= 0.16666667 0.5 0.5 0.16666667 /* " " */
Line 1,228 ⟶ 1,398:
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
tell: numeric digits digits()%2; say right(i, w) " " left('', $.i>=0)$.i /1; return</
{{out|output}}
<pre>
Line 1,255 ⟶ 1,425:
===version 2===
{{trans|Julia}}
<
Numeric Digits 24
acoef = '1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17'
Line 1,286 ⟶ 1,456:
ret.i=temp/a.1
Say format(i,2) format(ret.i,2,12)
End</
{{out|output}}
<pre> 1 -0.152973989500
Line 1,309 ⟶ 1,479:
20 0.651770838819
</pre>
=={{header|RPL}}==
We use here useful list handling functions that are available from HP48G or newer models.
{| class="wikitable"
! RPL code
! Comment
|-
|
≪
ROT REVLIST ROT REVLIST → signal a b
≪ { } 1 signal SIZE '''FOR''' j
signal j b SIZE - 1 + j SUB
'''WHILE''' DUP SIZE b SIZE < '''REPEAT''' 0 SWAP + '''END'''
b * ∑LIST
OVER j a SIZE - 1 + j 1 - SUB 0 +
'''WHILE''' DUP SIZE a SIZE < '''REPEAT''' 0 SWAP + '''END'''
a * ∑LIST -
a DUP SIZE GET / +
'''NEXT'''
≫ ≫ '<span style="color:blue">'''FILTR'''</span>' STO
|
<span style="color:blue">'''FILTR'''</span> ''( {a} {b} {signal} → {filtered} ) ''
Reverse a and b
For j = 1 to last signal item
extract what to multiply to b
prepend 0's if necessary
multiply by b and sum
extract what to multiply by a except a[0]
prepend 0's if necessary
multiply by a, sum and substract
divide by a[0] which is the last item once a reversed
|}
Figures have been rounded to 3 digits after the decimal point to ease the 100% manual data transfer.
{ 1 -2.778E-16 0.3333 -1.851E-17 }
{ 0.1667 0.5 0.5 0.1667}
{ -0.9178 0.1420 1.2054 0.1903 -0.6624
-1.007 -0.4047 0.8005 0.7435 1.0109
0.7415 0.2778 0.4008 -0.2086 -0.17281 -
-0.1343 0.02593 0.4901 0.5494 0.90472 }
<span style="color:blue">'''FILTR'''</span> 3 RND
'''Output:'''
<span style="color:grey"> 1:</span> { -.153 -.435 -.136 .697 .656
-.436 -1.089 -.538 .517 1.052
.962 .696 .425 .196 .028
-.212 -.175 .069 .386 .652 }
=={{header|Ruby}}==
{{trans|C#}}
<
result = Array.new(signal.length(), 0.0)
for i in 0..signal.length()-1 do
Line 1,352 ⟶ 1,569:
end
main()</
{{out}}
<pre>-0.15297399, -0.43525783, -0.13604340, 0.69750333, 0.65644469
Line 1,361 ⟶ 1,578:
=={{header|Rust}}==
{{trans|Java}}
<
struct IIRFilter<'f>(&'f [f32], &'f [f32]);
Line 1,462 ⟶ 1,679:
}
println!();
}</
{{out|output}}
<pre>
Line 1,478 ⟶ 1,695:
{{libheader|Scastie qualified}}
{{works with|Scala|2.13}}
<
private def filter(a: Vector[Double],
b: Vector[Double],
Line 1,513 ⟶ 1,730:
.foreach(line => println(line.mkString(" ")))
}</
=={{header|Sidef}}==
{{trans|Raku}}
<
var out = [0]*signal.len
for i in ^signal {
Line 1,542 ⟶ 1,759:
say "["
say f.map { "% 0.8f" % _ }.slices(5).map{.join(', ')}.join(",\n")
say "]"</
{{out}}
<pre>
Line 1,554 ⟶ 1,771:
=={{header|Visual Basic .NET}}==
{{trans|C#}}
<
Function Filter(a As Double(), b As Double(), signal As Double()) As Double()
Line 1,597 ⟶ 1,814:
End Sub
End Module</
{{out}}
<pre>-0.15297399, -0.43525783, -0.13604340, 0.69750333, 0.65644469
Line 1,603 ⟶ 1,820:
0.96185430, 0.69569009, 0.42435630, 0.19626223, -0.02783512
-0.21172192, -0.17474556, 0.06925841, 0.38544587, 0.65177084</pre>
=={{header|V (Vlang)}}==
{{trans|Go}}
<syntaxhighlight lang="v (vlang)">struct Filter {
b []f64
a []f64
}
fn (f Filter) filter(inp []f64) []f64 {
mut out := []f64{len: inp.len}
s := 1.0 / f.a[0]
for i in 0..inp.len {
mut tmp := 0.0
mut b := f.b
if i+1 < b.len {
b = b[..i+1]
}
for j, bj in b {
tmp += bj * inp[i-j]
}
mut a := f.a[1..]
if i < a.len {
a = a[..i]
}
for j, aj in a {
tmp -= aj * out[i-j-1]
}
out[i] = tmp * s
}
return out
}
//Constants for a Butterworth Filter (order 3, low pass)
const bwf = Filter{
a: [f64(1.00000000), -2.77555756e-16, 3.33333333e-01, -1.85037171e-17],
b: [f64(0.16666667), 0.5, 0.5, 0.16666667],
}
const sig = [
f64(-0.917843918645), 0.141984778794, 1.20536903482, 0.190286794412,
-0.662370894973, -1.00700480494, -0.404707073677, 0.800482325044,
0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195,
0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293,
0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589,
]
fn main() {
for v in bwf.filter(sig) {
println("${v:9.6}")
}
}</syntaxhighlight>
{{out}}
<pre>
-0.152974
-0.435258
-0.136043
0.697503
0.656445
-0.435482
-1.089239
-0.537677
0.517050
1.052250
0.961854
0.695690
0.424356
0.196262
-0.027835
-0.211722
-0.174746
0.069258
0.385446
0.651771
</pre>
=={{header|Wren}}==
{{trans|Kotlin}}
{{libheader|Wren-fmt}}
<
var filter = Fn.new { |a, b, signal|
Line 1,642 ⟶ 1,934:
Fmt.write("$11.8f", result[i])
System.write(((i + 1) % 5 != 0) ? ", " : "\n")
}</
{{out}}
<pre>
-0.15297399, -0.43525783, -0.13604340, 0.69750333, 0.65644469
-0.43548245, -1.08923946, -0.53767655, 0.51704999, 1.05224975
0.96185430, 0.69569009, 0.42435630, 0.19626223, -0.02783512
-0.21172192, -0.17474556, 0.06925841, 0.38544587, 0.65177084
</pre>
=={{header|XPL0}}==
<syntaxhighlight lang "XPL0">real A, B, Signal, Temp, Result(20);
int I, J;
[A:= [1.00000000, -2.77555756e-16, 3.33333333e-01, -1.85037171e-17];
B:= [0.16666667, 0.5, 0.5, 0.16666667];
Signal:= [
-0.917843918645, 0.141984778794, 1.20536903482, 0.190286794412,
-0.662370894973, -1.00700480494, -0.404707073677, 0.800482325044,
0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195,
0.400833448236, -0.2085993586, -0.172842103641, -0.134316096293,
0.0259303398477, 0.490105989562, 0.549391221511, 0.9047198589 ];
Format(2, 8);
for I:= 0 to 20-1 do
[Temp:= 0.;
for J:= 0 to 4-1 do
if I-J >= 0 then
Temp:= Temp + B(J)*Signal(I-J);
for J:= 1 to 4-1 do
if I-J >= 0 then
Temp:= Temp - A(J)*Result(I-J);
Result(I):= Temp / A(0);
RlOut(0, Result(I));
Text(0, if rem(I/5) = 4 then "^m^j" else ", ");
];
]</syntaxhighlight>
{{out}}
<pre>
Line 1,654 ⟶ 1,979:
=={{header|Yabasic}}==
{{trans|D}}
<
local i, j, tmp
Line 1,698 ⟶ 2,023:
print
end if
next</
=={{header|zkl}}==
{{trans|C++}}
<
out:=List.createLong(signal.len(),0.0); // vector of zeros
foreach i in (signal.len()){
Line 1,711 ⟶ 2,036:
}
out
}</
<
-0.662370894973,-1.00700480494, -0.404707073677, 0.800482325044,
0.743500089861, 1.01090520172, 0.741527555207, 0.277841675195,
Line 1,720 ⟶ 2,045:
b:=T(0.16666667, 0.5, 0.5, 0.16666667 );
result:=direct_form_II_transposed_filter(b,a,signal);
println(result);</
{{out}}
<pre>
|